I think the implicit assumptions about the “Police carry insurance” thing are:

1. Qualified immunity protections are replaced by insurance carriage
2. LEOs have to pay their own insurance (presumably with a pay hike that’s the “average” insurance payment

Without QI, LEOs would be liable. Insurance companies can certainly force LEOs to fight court cases, but the costs of doing so will fall on the insurance companies. An LEO that’s constantly a problem will find themselves in court a lot, and will end up costing the insurance company a lot, regardless of whether it’s just legal fees, or massive damages to their victims in addition to legal fees. So the insurer will force them to pay ever increasing premiums, and eventually they won’t be able to afford to be in law enforcement.

Most of what you’re saying would undermine the existing professional insurance requirements for doctors etc. Hell, it’d undermine insurance requirements for driving!

Also remember insurance companies rarely insure just one thing. You may get a carrier that specializes in LEOs, but in practice like most insurers it’ll cover a wide variety of different types of liability insurances, directly or indirectly. So it’s not necessarily in its best interests to defend LEOs regardless of what they’ve done. That just encourages bad law enforcement, pushing up its costs elsewhere.